The 2 Scottish Ceilidh Bands that I play in always finish the night (prior to Auld Lang Syne, of course!) with the Orcadian Strip the Willow, played to 6/8 jigs throughout. "Last Waltzes" have long since been dumped! If it's a really long line we may need to play the whole set of tunes twice through, or until the caller gives us the "cut throat" signal.
The "Strip the Willow" figure does occur in some other dances, including some versions of Virginia Reel (of which there are almost as many versions as callers!)